Question

Assume the random variable X is normally distributed with mean mu equals 50 and standard deviation sigma equals 7. Compute the probability. Be sure to draw a normal curve with the area corresponding to the probability shaded. Upper P (Upper X greater than 34 )

Answer 1

`P(X>34) = 0.9889`

Explanation:

We are given the following information in the question:

Mean, μ = 50

Standard Deviation, σ = 7

We are given that the distribution of random variable X is a bell shaped distribution that is a normal distribution.

Formula:

`z_(score) = \displaystyle(x-\mu)/(\sigma)`

P(X greater than 34)

`P( X > 34) = P( z > \displaystyle(34 - 50)/(7)) = P(z > -2.2857)`

`= 1 - P(z \leq -2.2857)`

Calculation the value from standard normal z table, we have,

`P(X>34) = 1 - 0.0111= 0.9889= 98.89\%`

The attached image shows the normal curve.